Comparatively speaking, it would be desirable to generalize the \(L^p\) -boundedness of the wave operators of Schrödinger operators to the fourth-order Schrödinger operator \(H=\Delta ^2+V(x)\) . In fact, until recently there exist several interesting works to study the resolvent \((H-z)^{-1}\)  and the decay estimates for \(e^{-itH}\)  (see e.g. [1]}, [2]}). Based on these recent works, Goldberg–Green [3]} first proved the \(L^p\) -boundedness of the wave operators for the fourth-order Schrödinger operator \(\Delta ^2+V(x)\)  on \({\mathbb {R}}^3\)  under the assumption that zero is a regular point. Furthermore, this result was extended by Erdoğan–Green [4]} to the higher-order Schrödinger operators \((-\Delta )^m+V\)  on \({\mathbb {R}}^n\)  for \(n> 2m\ge 4\)  again in the regular case.
